An analog quantum computer made of cold atoms used to simulate electrons’ spins

Precise modeling the complicated interactions between electrons in materials …

Many of the most exciting properties of materials arise due to interactions between electrons. Correlations between electrons' spins are involved in magnetism and may be responsible for high-temperature superconductivity—yet it's tough to get theory to match our experimental results. The major reason for the difficulty lies in how quickly they scale: the more interactions between spins, the more difficult it is to calculate their effects. As few as 30 interacting spins reaches the limits of modern computers.

Ironically, it turns out that the best way to model these quantum systems may be by using another quantum system. A promising new experiment demonstrates the simulation of hundreds of spins, using atoms as the simulation device.

In a crystal lattice, electron spins may interact with each other, which gives rise to the magnetic properties of a material. The more spins that interact within a solid, the more difficult it is to model the material exactly—even for 30 spins, the necessary level of processing pushes the limits of modern computing. Realistic materials contain far more than 30 atoms, but it won't be practical to simulate thousands of atoms for the foreseeable future.

A better method involves using atoms themselves to do the calculations. This type of analog computer was proposed by Richard Feynman in 1982, but it has taken advances in cooling and trapping atoms before the idea could be realized. (Analog computers, unlike their digital semiconductor-based cousins, simulate the equations of a physical system directly using electric circuits, oscillators, or—as in this case—controlled quantum states.) Simulating thousands of interacting spins only requires using thousands of atoms, a far more scalable option.

Joseph W. Britton et al. confined hundreds of beryllium atoms in an electromagnetic trap, creating an artificial lattice where the spins of the atoms could be controlled precisely. Each spin acts as a qubit (quantum bit) which falls into a binary state: spin-up or spin-down, analogous to the binary numbers 0 and 1 in ordinary logic. The interactions between the spins provided a good simulation of how they interact in a real material, while keeping them separate from other effects that are present in solids. While hundreds of atoms are still few compared to materials of realistic sizes, this experiment provides an excellent first step toward the large-scale quantum simulation of strongly correlated electron systems.

In their experiment, Britton et al. used a Penning trap, a special setup involving a combination of electric and magnetic fields. Between 100 and 350 beryllium ions (9Be+) were cooled using laser bombardment to dissipate their energy; once subjected to the electromagnetic fields, the ions naturally fell into a two-dimensional triangular lattice (as shown in the image above). The resulting "crystal" was approximately 0.3 millimeters across, and cooled nearly to absolute zero.

Ionization leaves one unpaired electron in the beryllium atoms. The spin of this lonely electron is the qubit, and the entire ion becomes a fermion, an object that obeys the Pauli exclusion principle, meaning two of them can't occupy the same state. The orientation of the spins either with or opposite to the magnetic field acts as a binary state, allowing them to probe the theory of magnetism in materials known as the Ising model.

While the magnetic field was used to control the orientation of all the spins, Britton et al. controlled the interaction strength and individual spin orientations using crossed lasers with different wavelengths. In this way, they could couple all spins to each other (a limiting case more than a realistic model), or limit the coupling to associations of the nearest neighbors. By keeping interaction strengths relatively small, they were able to compare how the atoms behaved to conventional approximations, thereby showing that their quantum simulator truly does reproduce the results expected from theory.

This experiment demonstrates that lattices of ions created by trapping are suitable for simulating complex quantum systems. Since such methods aren't particularly complicated by the standards of experimental atomic physics, it should be possible to test stronger interactions and spin configurations of different types. In this way, relatively simple configurations of large numbers of atoms can simulate far more complicated materials.